DETERMINING THE NUMBER OF WORK SAMPLE OBSERVATIONS NEEDED. The manager of Michigan County’s welfare office, Dana Johnson, estimates that her employees are idle 25% of the time. She would like to take a work sample that is accurate within ±3% and wants to have 95.45% confidence in the results.
APPROACH \blacktriangleright Dana applies Equation (10-7) to determine how many observations should be taken.
n = \frac{z^2 p(1 - p)}{h^2} (10-7)
SOLUTION \blacktriangleright Dana computes n:
n = \frac{z^2 p(1 – p)}{h^2}where n = required sample size
z = confidence level (2 for 95.45% confidence)
p = estimate of idle proportion = 25% = .25
h = acceptable error of 3% = .03
She finds that
n = \frac{(2)^2 (.25)(.75)}{(.03)^2} = 833 observations
INSIGHT \blacktriangleright Thus, 833 observations should be taken. If the percent of idle time observed is not close to 25% as the study progresses, then the number of observations may have to be recalculated and increased or decreased as appropriate.
LEARNING EXERCISE \blacktriangleright If the confidence level increases to 99.73%, how does the sample size change? [Answer: n = 1,875.]
RELATED PROBLEMS \blacktriangleright 10.31, 10.32, 10.35, 10.37
ACTIVE MODEL 10.1 This example is further illustrated in Active Model 10.1 in MyOMLab.